Existence of Infinitely Many Solutions for a Quasilinear Elliptic Problem on Time Scales

TL;DR

This paper investigates a boundary-value quasilinear elliptic problem on arbitrary time scales, establishing conditions for the existence, multiplicity, and infinite solutions of positive solutions using fixed-point index theory.

Contribution

It introduces new sufficient conditions for positive solutions of quasilinear elliptic problems on time scales, extending classical results to a more general setting.

Findings

Conditions for existence of solutions

Criteria for multiple solutions

Proof of infinite solutions under certain conditions

Abstract

We study a boundary-value quasilinear elliptic problem on a generic time scale. Making use of the fixed-point index theory, sufficient conditions are given to obtain existence, multiplicity, and infinite solvability of positive solutions.